Dielectric hysteresis in piezoceramic transducers can degrade their performance in structural vibration control applications. Different hysteresis models have been applied to piezoelectric transducers, including those based on Preisach, Jiles-Atherton and Ishlinskii concepts. Relationships between these and other models, new experimental identification schemes and multi-term describing function representations of some of them are reviewed. Then, system equations that incorporate the hysteretic behavior are formulated for two pedagogical smart structural systems: a passively shunted / actively driven PZT wafer on (1) a simply supported thin plate and (2) a simply supported thin beam. The effect of PZT hysteresis on optimized passive and hybrid vibration control strategies is evaluated.